where \(\mathbb {L}\)  is the set of ideologies (in our case, left or right) and \(p_l\)  is the fraction of \(u\) 's followees \(w\)  weeks after treatment who have ideology \(l\in \mathbb {L}\)Note that our computation of network diversity here is slightly different than the computation used to display to users their connection diversity scores during treatment. In particular, the displayed scores are computed a) using only their connections in the sampled network of 32k users, not their entire set of followees on Twitter, and b) using terms weighted by the PageRank of the account followed in the sampled network - so that following higher-PageRanking accounts of one ideology versus another leads to a score less than 1 even if the absolute number of connections belonging to either ideology are equivalent.. We leverage the political classifier presented in [1]} to estimate the likelihood of a given Twitter account leaning left or right and use a 60% threshold to assign final ideology labelsWe use a binary ideological classification scheme for simplicity, though one opportunity for future work includes conducting a similar study with a more flexible, continuous notion of ideology..
